Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory

Stojanović, Vladimir; Kozić, Predrag; Janevski, Goran

doi:10.1016/j.jsv.2012.09.005

Cited by 53 publications

(27 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mathematical expressions of the boundary conditions for simply supported i-th nanoplate are given as [52],…”

Section: Problem Formulation and Closed Form Solutionmentioning

confidence: 99%

“…In the recently published works by Karličić et al [49] and Stojanović et al [52], the methodology to obtain analytical solutions for natural frequencies and critical buckling loads of complex systems of homogeneous and elastic beams and plates is suggested. Based on these results, we supposed the solution of ith algebraic equation in the system (17) …”

Section: Problem Formulation and Closed Form Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

Karličić

Cajić

Kozić

et al. 2015

Composite Structures

Self Cite

View full text Add to dashboard Cite

“…Mathematical expressions of the boundary conditions for simply supported i-th nanoplate are given as [52],…”

Section: Problem Formulation and Closed Form Solutionmentioning

confidence: 99%

Section: Problem Formulation and Closed Form Solutionmentioning

confidence: 99%

Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

Karličić

Cajić

Kozić

et al. 2015

Composite Structures

Self Cite

View full text Add to dashboard Cite

“…Based on works by Ra sković, 70 Stojanović et al 71 and Karličić et al 72 we propose the solution of i À th algebraic equation in the following form: Substituting Eq. (21) into the i À th algebraic equation of the system (20), and after some algebra, we obtain two trigonometric equations with the assumption that constants M and N are not simultaneously equal to zero…”

Section: Exact Solution For Complex Natural Frequencymentioning

confidence: 99%

Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field

Karličić¹,

Murmu

Cajić³

et al. 2014

Journal of Applied Physics

Self Cite

View full text Add to dashboard Cite

Nanocomposites and magnetic field effects on nanostructures have received great attention in recent years. A large amount of research work was focused on developing the proper theoretical framework for describing many physical effects appearing in structures on nanoscale level. Great step in this direction was successful application of nonlocal continuum field theory of Eringen. In the present paper, the free transverse vibration analysis is carried out for the system composed of multiple single walled carbon nanotubes (MSWCNT) embedded in a polymer matrix and under the influence of an axial magnetic field. Equivalent nonlocal model of MSWCNT is adopted as viscoelastically coupled multi-nanobeam system (MNBS) under the influence of longitudinal magnetic field. Governing equations of motion are derived using the Newton second low and nonlocal Rayleigh beam theory, which take into account small-scale effects, the effect of nanobeam angular acceleration, internal damping and Maxwell relation. Explicit expressions for complex natural frequency are derived based on the method of separation of variables and trigonometric method for the “Clamped-Chain” system. In addition, an analytical method is proposed in order to obtain asymptotic damped natural frequency and the critical damping ratio, which are independent of boundary conditions and a number of nanobeams in MNBS. The validity of obtained results is confirmed by comparing the results obtained for complex frequencies via trigonometric method with the results obtained by using numerical methods. The influence of the longitudinal magnetic field on the free vibration response of viscoelastically coupled MNBS is discussed in detail. In addition, numerical results are presented to point out the effects of the nonlocal parameter, internal damping, and parameters of viscoelastic medium on complex natural frequencies of the system. The results demonstrate the efficiency of the suggested methodology to find the closed form solutions for the free vibration response of multiple nanostructure systems under the influence of magnetic field.

show abstract

“…The Timoshenko beam theory is applied as a base for more complex problems, like beam vibrations on elastic foundation (De Rosa 1995), beam vibrations and buckling on elastic foundation (Matsunaga 1999), vibrations of double-beam system with transverse and axial load (Stojanović and Kozić 2012), vibration and stability of multiple beam systems (Stojanović et al 2013), beam response moving to load (Sniady 2008), etc. Recently, the Timoshenko beam theory is used in nanotechnology for vibration analysis of nanotubes, as for instance (Simsek 2011).…”

Section: Introductionmentioning

confidence: 99%

Physical insight into Timoshenko beam theory and its modification with extension

Senjanović¹,

Vladimir²

2013

Structural Engineering and Mechanics

View full text Add to dashboard Cite

Abstract. An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

show abstract

Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory

Cited by 53 publications

References 9 publications

Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field

Physical insight into Timoshenko beam theory and its modification with extension

Contact Info

Product

Resources

About